"surfaces of revolution," as they are called. These are the paraboloid, the ellipsoid, and the hyperboloid of revolution. The paraboloid of revolution is of importance in optics, as it is used in some specula for telescopes. See arts. SPECULUM and TELESCOPE. The three surfaces last named are, however, all of them interesting, as being for pencils of light incident in certain ways what are called surfaces of accurate reflection-i.e., they reflect all the rays of the incident pencil to a single point or focus. We shall explain to what this property is owing in the case of the parabolic reflector, and state generally the facts regarding the other two. 1. The concave parabolic reflector is a surface of accurate reflection for pencils of rays parallel to the axis or central line of figure of the paraboloid. This results from the property of the surface, that the normal at any point of it passes through the axis, and bisects the angle between a line through that point, parallel to the axis, and a line joining the point to the focus of the generating parabola. Referring to fig. 6, suppose a ray incident on the surface at P, in the line SP, parallel to the axis AFG. Then if F be the focus of the generating parabola, join PF. PF is the direction of the reflected ray. For PG, the normal at P, by the property of the surface, bisects the angle FPS, and thereforo (angle) FPG=GPS. But SPG is the angle of incidence, and SP, PG, and FP are in one plane, and, therefore, by the laws of reflection, FP is the reflected ray. In the same way, all rays whatever, parallel to the axis, must pass through F after reflection. If F were a luminous point, the rays from it, after reflection on the mirror, would all proceed in a cylindrical pencil parallel to the axis. This reflector, with a bright light in its focus, is accordingly of common use in light houses. 2. In the concave ellipsoid mirror there are two points-viz., the foci of the generating ellipse, such that rays diverging from either will be accurately reflected to the other. This results from the property of the figure, that the normal at any point bisects the angle included between lines drawn to that point from the foci. 3. Owing to a property of the surface similar to that of the ellipsoid, a pencil of rays converging to the exterior focus of a hyperbolic reflector, will be accurately reflected to the focus of the generating hyperbola. The converse of the above three propositions holds in the case of the mirrors being convex. Though the sphere is not a surface of accurate reflection, except for rays diverging from the center, and which on reflection are returned thereto, the spherical reflector is of great practical importance, because it can be made with greater facility and at less expense than the parabolic reflector. See art. TELESCOPE. It is necessary, then, to investigate the phenomena of light reflected from it. 4. Spherical Mirrors.—It is usual to treat of two cases, the one the more frequent in practice, the other the more general and comprehensive in theory. First, then, to find the focus of reflected rays when a small pencil of parallel rays is incident directly on a concave spherical mirror. Let BAB' (fig. 7) be a section of the mirror, O its center of curvature, and A. the center of its aperture. AO is the axis of the mirror, and therefore of the incident pencil, because it is incident directly on the mirror; a pencil being called oblique when its axis is at an angle to the axis of the mirror. As the ray incident in the line OA will be reflected back in the same line-OA being the normal at A— the focus of reflected rays must be in OA. Let SP be one of the rays; it will be reflected so that qPO= SPO. But 4 POq= / OPS by parallel lines. Therefore, 4 qPO= gOP, and Pq and Oq are equal. If, now, the incident pencil be very small-i.e., if P be very near A-then the line Pq will very nearly coincide with the line OA, and Pq and Oq will each of them become very nearly the half of OA. Let F be the middle point of OA-the point, namely, to which q tends as the pencil diminishes. The F is called the principal focus of the mirror, and AF the principal focal length, which is thus = radius of the mirror. It will be observed that when AP is not small, q lies between A and F. Fq is called the aberration of the ray. When AP is large, the reflected rays will continually intersect, and form a luminous curve with a cusp at F. This curve is called the caustic (q.v.). We shall now proceed to the more general case of a small pencil of diverging rays, incident directly on a concave spherical mirror. Let PAP' (fig. 8) be a section of the mirror, A the center of its aperture, O of its curvature, and let F be its principal focus. Then, if Q be the focus of incident rays (as if proceeding from a candle there situated), q, the focus of the reflected rays, lies on QOA, since the pencil is incident directly, and the ray QOA, being incident in the line of the normal ÚA, is reflected back in the same line. Let PQ be any other ray of the pencil. It will be reflected in Pq, so that ≤ qPO= /OPQ; and on the supposition that PA is very small, so that QP becomes nearly equal to QA, and qP to qA, it can be shown, by Euclid, vi. 3, QO_qo QA XAF that = very nearly. From this equation is deduced the formula qA : QAqA which enables us to find qA, when QA and AF are known. Thus, let the radius of curvature be 12 in., and the distance of the source of the rays, or QA, 30 in., the focal 30 × 6 19 Fig. 9. = = QA-AF 7 inches. If the rays had diverged upon q, it is clear they would have been reflected to Q. The points Q and q, accord If the mirror be convex, as in fig. 9, instead of concave, and a pencil of diverging rays be incident directly on it from Q, we should find, proceeding in exactly the same way as in the former case, the equation Ag = QAX AF same numbers as before; qA: = 30 X 6 or taking the = 5 inches. For information regarding the formation of images by spherical mirrors, the reader may consult Potter's Elements of Optics. See also the arts. MIRRORS and IMAGES. By considering fig. 8, it is easy to see how the relative positions of the two conjugate foci, as they are called, Q and q, vary as the distance, AQ, of the origin of the rays is changed. As Q is advanced towards O, q also approaches O, since the angles QPO and qPO always remain equal; and when the source of the light is in the center, O, of the sphere, the reflected rays are all returned upon the source. As Q, again, recedes from O, q moves towards F, which it does not quite reach until the distance of Qis infinite, so that the incident rays may be considered as parallel, as in fig. 7. If Q is placed between O and F, then q will be to the right of O; and when Q coincides with F, the reflected rays will have no focus, but will be parallel. If Q is between F and A, the reflected rays will diverge, and will have their virtual focus to the left of A. The correctness of these deductions may easily be verified. The positions of the conjugates are traced in precisely the same way for the convex mirror, and the reader who is interested will find no difficulty in tracing them for himself. CATOP TROMANCY, divination by the mirror or looking-glass. At Patras, in Greece, the sick foretold their death or recovery by means of a mirror let down with a thread until its base touched the water in a fountain before the temple of Ceres. The face of the sick person appearing healthy in the mirror, betokened recovery; if it looked ghastly, then death was sure to ensue. More modern superstitions attach ill-luck to the breaking of a looking-glass, and to seeing one's face in a glass by candle-light. CATS, JACOB, a Dutch statesman and poet, was b. at Brouwershaven, in Zeeland, in 1577, and after studying law, finally settled at Middelburg. He rose to high offices in the state, and was twice sent as ambassador to England, first in 1627, and again in 1652, while Cromwell was at the head of affairs. He died 1660. As a poet, he enjoyed the highest popularity. His poems are characterized by simplicity, rich fancy, clearness, and purity of style, and excellent moral tendency. The most highly prized of his productions were the Huwelyk, Trouwringh (a series of romantic stories relating to remarkable marriages), and the Spiegel van den Ouden in Nieuwen Tyd. The best edition of his works appeared at Amsterdam, in 19 vols., 1790-1800. CAT'S-EYE, a beautiful mineral, a variety of quartz receiving its name from the resemblance which the reflection of light from it, especially when cut en cabochon, or in a convex form, is supposed to exhibit to the light which seems to emanate from the interior of the eye of a cat. It has a sort of pearly appearance, and is chatoyant or characterized by a fine play of light, which results from the parallel arrangement of the minute fibers of the stone itself, or from an intimate mixture of some foreign substance, such as amianthus. It has been supposed that cat's-eye is silicified wood. It is of various colors, and is obtained chiefly from Malabar and Ceylon. The Singl:alese are especially proud of it, believing it, although erroneously, to be only found in their island. It is often brought from that island, cut to resemble a monkey's face, from the idolatrous regard entertained for the monkey. CATSKILL, capital of Greene co., N. Y., on the w. bank of the Hudson, at the mouth of Catskill creek, 34 m. s. of Albany. Pop. '80, 8311. It is on the West Shore railroad; is the starting point of a railroad to the Catskill mountains, and is connected with the Hudson River railroad by a ferry to Catskill station. It has a court house, opera house, free academy, 2 national banks, 7 churches, large hotels, 4 handsome bridges, and manufactures of woolens, paper, etc. CATSKILL GROUP, in geology, the name of rocks of the Devonian system seen in the northern counties of Pennsylvania. They are chiefly red sandstone and shale, and contain fossil scales of the earliest fishes. The Catskill mountains were formerly supposed to belong in this group, whence the name, now known to be inappropriate. CATSKILL MOUNTAINS, a group of the Alleghany chain, in its largest sense, situated near the right bank at once of the Hudson and of the Mohawk, in the state of New York. The loftiest points, Round Top and High Peak, are respectively 3,800 ft. and 3,720 above tide-water; and, on a third eminence, a terrace of 2,231 ft. above the same level presents Catskill Mountain house, a favorite retreat in summer. The group is drained chiefly by Catskill creek, which, at a village of its own name, enters the Hudson 111 m. above its mouth, and 34 below the confluence of the Mohawk. CATSKILL MOUNTAINS, a part of the Appalachian system w. of the Hudson river, mostly in Greene co., N. Y. The group, about 12 m. long, nearly parallel with the river about, 8 m. distant, turns westward in spurs extending many miles. Besides the Ulster and Delaware railroad, beginning at Kingston and leading w. into the mountains, there is a good wagon road from Catskill village to the "Mountain House," 12 m. w., which is a favorite summering place. The house stands on a terrace 2,231 ft. above the river, and almost at the edge of a perpendicular cliff several hundred ft. high. There is another public house on Overlook mountain, a few miles to the s., which is estimated to be 3,800 ft. above tide. The views from these houses and from the neighboring peaks are wonderfully varied and beautiful, reaching from the Green mountains in Vermont to the highlands at West Point, and taking in nearly 100 m. of the Hudson river and valley, with numerous cities and villages, and a vast expanse of highly cultivated farming country. An immense number of summer boarders are accommodated through all this region, not only in hotels, but also in countless farm-houses and village homes. One of the highest points is the top of Overlook, 3,800 feet. The other prominent elevations are Hunter mountain, High peak, and Round Top. One of the sights of the region is "The Clove," or ravine, and the falls therein. The ravine is about 5 m. long. At its head two rivulets unite and flow rapidly to a point where the mountain divides and forms a deep hollow into which the brook rushes over a cascade of 180 ft.; and further down are other falls, one of 80 and another of 40 feet. The ice formation in winter around the highest fall is particularly grand and beautiful. There are other ravines and water-falls in the region, but none equally important. The mountains are for the most part covered with thick forests of oak, hickory, ash, maple, beech, pine, etc. CAT'S-TAIL. See TYPHA. CAT'S-TAIL GRASS. See TIMOTHY GRASS. CATTACK. See CUTTACK. CATTARAUGUS, a co. in w. New York, on the Pennsylvania border, watered by the Allegheny and other rivers, and intersected by the New York and Erie and the Atlantic and Great Western railroads, and the Genesee Valley canal; 1250 sq.m.; pop. '80, 55,808. The surface is undulating and the soil fruitful. The chief products are wheat, corn, oats, potatoes, hay, cheese, butter, wool, hops, and maple sugar. Iron, manganese, marl, peat, and sulphur are found. Co. seat, Little Valley. CAT TARO, a t. of Austria, in the crown-land of Dalmatia, is situated at the head of the gulf of Cattaro, about 36 m. s.e. of Ragusa. It is strongly fortified, and surrounded on all sides by mountains. The castle, a massive and almost inaccessible building, stands on a precipitous rock immediately behind the town. C. has a cathedral several churches and hospitals, and a population of 3,000. C., which was at one time the capital of a small republic, was in 1807 annexed to the kingdom of Italy, but was handed over to Austria in 1814 by the treaty of Vienna.-CATTARO, GULF OF, or BOCCA DI CATTARO, an inlet of the Adriatic, near the s. extremity of the Dalmatian coast. It consists of three basins or lakes, connected by straits of about half a mile in breadth. The outer entrance is only a mile and a half wide, and the total length of the gulf is about 30 miles. Mountains protect it from all winds, and it has a depth of from 15 to 20 fathoms. CAT TEGAT, or KATTEGAT (Sinus Codanus), the bay or arm of the sea situated between the e. coast of Jütland and the w. coast of Sweden, to the n. of the Danish islands. It is connected with the Baltic sea by the Great and Little Belt (q.v.), and by the sound. The Skager Rack (q. v.) connects it with the North sea. The length of the C. is about 150 m, and its greatest breadth 85 miles. It is of unequal depth, and has dangerous sand-banks. The principal islands are Lasöe, Samsoe, and Anhalt. The Danish shores of the C. are low, but the Swedish shore is very steep and rocky. CATTERMOLE, GEORGE, one of the most distinguished of English painters in watercolors, was born at Dickleburgh, Norfolk, in 1800. His pictures, which embrace a wide range of subjects, are remarkable for their striking originality of conception, vigorous execution, and fine color and tone. One of his best known and greatest pictures is "Luther at the Diet of Spires," containing 33 portraits of the principal characters, copied from the authentic originals by the old masters. He also designed the engravings for his brother's History of the Civil Wars, and illustrated many scenes in Scott's novels and in Shakespeare. His later works are chiefly oil-paintings. He d. July 24, 1868. CATTI, or CHATTI, a German people, included by Cæsar under the name Suevi (q.v.), who inhabited a country pretty nearly corresponding to the present Hesse. The southwestern part of their territory, around Mattiacum, was conquered by the Romans under Drusus. The C. took part in the general rising of the Germans under Hermann. Tacitus praises them as excellent foot-soldiers. During the reign of Marcus Aurelius, in the end of the 2d c., they made incursions into Roman Germany and Rhætia. Caracalla failed in an expedition against them and the Alemanni in the 3d century. About the middle of that century, their name began to give place to that of the Franks (q.v.), and is last mentioned by Claudian in the latter part of the 4th century. CATTLE. See Ox. CATTLE, in English law. See CHATTEL. *CATTLE-PLAGUE, RINDERPEST (Ger.), or STEPPE MURRAIN, is a contagious eruptive fever, or exanthema, of the bovine species; sheep, goats, deer, and other allied species occasionally, however, catch it from cattle. It occurs indigenously on the plains of western Russia, whence it has at various times overspread most parts of the old world. The specific virus from diseased or infected animals is the only source of cattle-plague; no filth, overcrowding, or other health-depressing cause has hitherto produced it. As in small-pox, scarlatina, and other eruptive fevers, an incubative stage, varying between two and twenty days, intervenes between the introduction of the virus into the system, either by inoculation or contagion, and the development of the characteristic symptoms. These consist essentially of congestion of the mucous and cutaneous surfaces, with a sort of aphthous eruption, and thickening, softening, and desquamation of the superficial investing membrane. The disease runs a tolerably fixed and definite course, which is not materially altered by any known remedial measures. It seldom attacks the same individual a second time. History.-The cattle-plague has been recognized for upwards of a thousand years. It appears to have destroyed the herds of the warlike tribes who overran the Roman empire during the 4th and 5th centuries. About 810, it traveled with the armies of Charlemagne into France, and about the same period is also supposed to have visited England. Several times throughout the course of every century it spread from the plains of Russia over the western countries of Europe, and is stated to have again visited England about 1225. Although occasioning, every few years, great losses on the continent of Europe, the plague does not appear to have again shown itself in England until 1714, when it appeared at Islington about the middle of July, was very destructive for about three months, but was again got rid of towards Christmas. In 1744, it was in Holland, destroying there, in two years, 200,000 cattle; in Denmark, from 1745-49, it killed 280,000; in some provinces of Sweden it spared only 2 per cent of the horned cattle. It made terrible havoc throughout Italy, destroying 400,000 beasts in Piedmont alone. In April, 1745, the plague was again imported into England, probably by some white calves from Holland, where, as already stated, it had for some time prevailed. It continued its devastations for twelve years, but it is now impossible accurately to discover the losses it occasioned. In the third and fourth years of its ravages, 80,000 cattle were slaughtered, and double that number are supposed to have died. In 1747, 40,000 cattle died in Nottingham and Lancashire alone; whilst, so late as 1757, 30,000 perished in Cheshire in six months. In March, 1770, the disease was brought with some hay from Holland to Portsoy, in the Moray firth; several cattle died, and others, to the value of £799, 128. 2d., being destroyed, the further spread of the pest was prevented. By the wars which wasted Europe towards the close of the last and first eighteen years of the present century, cattle-plague was spread widely over the continent, and occasioned, wherever it occurred, terrible losses. Since then, at short intervals, it has spread-always being traceable to its source on the Russian plains-over Poland, Hungary, Austria, Prussia, portions of Germany and Italy, and has extended to Egypt. It has also reached China and Japan. The British outbreak of 1865-67, like its predecessors, undoubtedly came from Russia. The steamer Tonning, from Revel, brought 331 cattle and 330 sheep into Hull on 29th May, 1865. A portion of the cattle had come from the interior of Russia, where the plague then was, or recently had been; the cargo was rapidly landed, and very hurriedly inspected. Nearly half of the cattle were distributed in various lots to butchers in Leeds, Derby, and Manchester, but, curiously, these do not appear to have left any contagion in their trail. One hundred and seventy-five came to London, remained from the Monday evening until Thursday's market in lairs at York road, adjoining the cattle-market. It was stated, in a leader in the Times of 15th Aug., that rinderpest was seen in the metropolitan market as early as 12th June. Certain it is that more than one lot purchased on 19th June carried the disease to several dairies in and about London. The first cases were mistaken for cases of poisoning, the cows they had stood beside were sent into market, and thus the subtle disorder in a few weeks spread into many dairies both in town and country. Twenty-three Dutch cattle, having stood over for several markets, were sent back to Holland on 2d July, carried with them the contagion, were placed in a field near Schiedam, but soon sickened and died, thus spreading the disease in Holland. During the next six months, plague was repeatedly reimported thence into England. Until 11th Aug., 1865, no restrictions whatever were Cattle, put upon the removal of cattle; diseased and infected animals were freely taken to fairs and markets, were openly traveled by road and rail; whilst the metropolitan market continued every week to send forth infected cases, not only to the neighboring counties, but to Southampton, Birmingham, Hereford, Liverpool, Edinburgh, and even to Aberdeenshire. As early as 18th July, the pest was brought from London to Huntly by four calves; subsequent outbreaks occurred in the same way. The stamping-out system was, however, early and rigidly enforced in Aberdeenshire, and eight distinct outbreaks were promptly got rid of. In Edinburgh, it appeared probably about 9th Aug., was brought from London by some low-priced foreign cows; in six weeks, about 800, or one half the dairy cows in Edinburgh, had died-200 having been buried in one trench. By the end of Jan., four fifths of the dairy cows had perished, but Edinburgh was reported clear. In Glasgow, the first case occurred on 19th Aug., in a cow sent from Edinburgh. By 30th Sept., 432 cases were reported, and it continued to spread. By the middle of Oct., it was in Mr. Harvey's valuable stock of 800, of which 25 died in one night, and to save further loss, 50 healthy animals were in one day disposed of to the butcher. From Falkirk Trysts, as from Barnet, Norwich Hill, and other large English fairs, the disease was transmitted into fresh localities. From the autumn trysts, it was carried into Perthshire, Forfarshire, and Fifeshire. Diseased cattle passing along in railway trucks, appear to have spread the contagion over the fields adjoining the line at Thornton, Fifeshire. Into West Lothian it was conveyed in early Sept. by lambs from the Edinburgh market. The rapid spread of the insidious disorder may be gathered from the fact that, whilst, during the week ending 24th June, 1865, there was only one outbreak at Mrs. Nicholl's dairy at Islington, and 30 animals affected, by 30th Sept. there were 1703 farms, sheds, or other places in which the pest had appeared, and 13,263 animals had been attacked. Three months later, 8252 separate places had been visited, and 62,743 animals attacked. During six months, the aggregate of cattle attacked was 76,002. During the three months to 30th Mar., 13,443 farms and other premises had been infected, and 147,275 cattle attacked. In Dec., 1865, the fresh cases each week reached 9000; but in spite of remedial and preventive measures, of orders in council, and restrictions on the movement of stock, the number of weekly cases steadily increased to 15,706 in the third week of Feb. "The cattle diseases prevention act" passed 20th Feb., 1866, and the advantages flowing from the restrictions thus tardily imposed on the trade in cattle, and the slaughter of diseased and infected animals, were speedily apparent. In four weeks, the number of cases was reduced by one half. During the three months ending 30th June, 28,276 cases were reported; during the next three months to 30th Sept., the numbers fell to 2108; whilst, to 29th Dec., the three months' cases were but 149; to 30th Mar., 1867, 89 new cases were noted. Throughout April and May the number of cases continued steadily to decline; but during the week ending 25th May a fresh outbreak occurred in the Finsbury district of the metropolis, and 81 animals died, or were slaughtered to prevent the further spread of the pest. With the exception of an isolated outbreak in Essex, which was promptly stayed by slaughter of the ailing and suspected animals, the country was free of plague during August. The following are the records of its destructive career during 1865-67: To this sad total must be added 11,000 cases known to have been attacked and unaccounted for, and upwards of 60,000 healthy cattle slaughtered to prevent the spread of the disease. Plague was again imported into Hull in Aug., 1872; it was brought with cattle from Cronstadt; it spread into several districts of the East Riding, attacked 72 animals, 51 of which were killed, and 21 died. In 1877, an outbreak took place in Germany, but by energetic measures was speedily suppressed without extensive losses. Causes.-The development of cattle-plague by filth, overcrowding, miasmata, hot weather, or other such causes, is untenable. Faulty hygiene, by lowering vitality, probably renders the animal more prone to the attack, and less able to bear up against it, but it cannot originate plague. Like hydrophobia, small-pox, or syphilis, it is developed only by the special virus, which appears to have its habitat on the Russian steppes. This virus occurs abundantly in the blood of every plague-stricken beast, in the discharges from its nostrils, mouth, or eyes, in the off-scourings from the bowels, probably even in the breath. It may be transferred to healthy beasts by inoculation. A little of the blood or nasal or other mucous discharges of a plague case, if introduced underneath the skin of a healthy cow, develops the disease within a few days. The transference of the virus or contagion from the sick to the sound animal, is not always so direct and evident. As with other catching diseases, the virus may be carried considerable distances in the air; its particles are minute. but they have powerful vitality; it may adhere to the food that has lain before infected beasts; to the litter from the stalls, or even after it has been heaped for weeks; to the clothes of attendants; to the floors, walls, or stalling of build |